What is the Square Root of 8?

Date: Thu, 13 Jun 1996 21:29:18 -0400 (EDT)
From: Dr. Tom
Subject: Re: square routes
>what is the square route of 8?
First off, it's "square root", not "square route".
If you just punch it into your calculator, you'll get something like:
2.8284271247461900976, and this is not even EXACTLY right.
The square root of a number is some other number which, when
multiplied by itself, gives the original number.
The square root of 9 is 3 since 3 times 3 is 9.
If you multiply the number 2.82... above by itself, you don't get
quite 8; you get 7.99999999999999999998... But by adding more
and more decimal places, you can get numbers closer and closer to
the real square root.
This is not unusual -- what is 1/3, after all? Is it .333, or
.33333333, or .333333333333333333333333? It's none of those,
but the last is quite close to the exact value.
You can find approximate square roots by trial and error:
for sqrt(8), 2 is too small and 3 is too big, so try 2.5, 2.6, 2.7, 2.8,
and 2.9. You'll find the answer is between 2.8 and 2.9. So then try
2.81, 2.82, ... et cetera, to see that it's between 2.82 and 2.83, and
so on.
Or you can just use a calculator or computer!
-Doctor Tom, The Math Forum